The striker, 29, has spent the last two days in hospital after being taken ill following the 3-2 win over Roma.
Reports from Italian news agency Ansa claimed he had suffered a stroke.
Allegri said: "We'll be playing for Antonio. Quite apart from the sporting element, what counts most is the human aspect and we're all feeling sad."
Cassano had complained of finding it difficult to speak or move when the team arrived back in Milan in the early hours of Sunday morning.
He has since been undergoing tests on his heart and brain in hospital.Continue reading the main story Bari (1999-2001) 48 league games, six goalsRoma (2001-06) 118 games, 39 goalsReal Madrid (2006-08) 19 games, two goalsSampdoria (loan 2007-08) 22 games, 10 goalsSampdoria (2008-11) 96 games, 35 goalsAC Milan (2011-) 26 games, eight goals
Allegri added: "Antonio was doing well and he was in good shape and I hope he'll be back as soon as possible.
"The doctors are working on it, let's hope it all goes well.
"I can't diagnose him but he sounds fine. It was completely unexpected and has nothing to do with football. Let's leave it to the doctors and I think everything will be fine."
Luton defender Sol Davis had a stroke in 2006 but was able to return to the first team two months later.
Milan are top of Champions League Group H after drawing with Barcelona and beating BATE Borisov and Viktoria Plzen so far.